Analog filters having well-defined and steep transition bands (the range of frequencies where the filter goes from passing the signal to blocking the signal) can be complex and costly. The components of such filters may be hard to match, particularly on a single silicon chip because the transfer function, as represented in a pole-zero analysis, requires many poles and/or zeros which must all match. As the filler order increases, i.e., as more poles and zeros are required, the Q of the filter (the bandwidth relative to the center frequency) typically increases, and high-Q circuits require low noise and high dynamic range.
Some such analog applications, for example a band limiting filter such as a television channel select filter (CSF), may be commonly done with an expensive surface acoustic wave (SAW) device. However, such devices may have reliability issues due to the need to interconnect from the SAW device to a silicon chip, as well as insertion losses, which typically require a high performance amplifier to compensate. Thus, alternatives have been sought to such complex analog filters.
One technique that is common in digital signal processing is a finite impulse response (FIR) filter, which is well known in the prior art. One type of FIR filter is a transversal filter, or tapped delay line filter, as shown in FIG. 1. The output of such a filter is a weighted combination of voltages taken from uniformly spaced taps, and thus a weighted sum of the current input value and a finite number of previous values of the input. The output is proportional to the sum of the delayed voltages divided by the resistances connected to the respective voltages. The proportionality of the output is thus a constant, the constant being the parallel impedance of all the resistances.
The filter contains a plurality (here 7 are shown) of unit delay elements U1 to U7, each of which introduces a delay of time t. Delay elements U1 to U7 are all clocked by the same clock, so that the input signal propagates at a desired sampling rate. The filter is considered to be of the Mth order, where M−1 is the number of delay elements, so the filter of FIG. 1 is an 8th order filter. The output of each of the delay elements U1 to U7 is connected to an element having impedance, here shown as a resistor R1 to R7, typically through some buffering means, such as buffers Z1 to Z7. The resistors all share a common output point. (Other elements having impedance may be used rather than resistors, such as for example, capacitors or inductors.)
As an input signal Sn progresses through the delay elements, its contribution to the output voltage varies in time; each resistor causes the signal on the respective delay element to which it is attached to contribute to the output signal in inverse proportion to the resistor value. Thus, if the resistor is small, the signal on the attached delay element will have a large contribution to the output voltage, while if the resistor is large the contribution to the output will be smaller.
It is well known that the basis of a FIR filter is the mathematics of Fourier transforms. By properly selecting the resistor values in a set of resistors as the inverse of a set of Fourier coefficients that is calculated to provide a desired frequency response, a FIR filter is designed to provide an output with that response. The resistor values are typically calculated by a software program which takes the desired frequency response as an input.
The output of a FIR filter is thus generally characterized, by the expression:
  Out  =            ∑              i        =        0            W        ⁢                  In        i            *              W        i            where N is the number of elements in the filter, the values of Wi represent the set of weighting factors implemented by the resistors, and the values of Ini represent a series of delayed versions of the input signal.
In a typical FIR filter, the delay between each value of Ini may be, for example, 1 nanosecond (nS), and the filter may consist of, for example, 30 elements or more. However, this a broad generalization, and there are many variations of both the delay time and the number of elements that are known to those of skill in the art.
The values of Wi and Ini may be continuous, i.e., analog quantities, or may be quantized, i.e., digital or digitally encoded quantities. However, one limitation on an “all analog” FIR filter is the delay elements: although a transmission line is an easy way to implement such delay elements, such a line is impractical to implement on a silicon chip.
One way to avoid this limitation is to use a digital representation of the input signal, i.e., to use values of Ini that are digital quantities which may be easily delayed in a logic circuit; the precise analog signal is not important since all that is necessary to encode a digital signal is whether the signal is high or low relative to some threshold and thus results in a 1 or a 0. A FIR filter built in this way, where the values of to are digital and the values of Wi are analog, is commonly referred to as a semi-analog FIR filter.
A semi-analog FIR filter is advantageous since it replaces the delay elements that would need to be analog-in and analog-out with clocked digital delay elements. Such digital delay elements impose two degrees of quantization on the analog signal. First, since the delay elements are clocked, they can only change state on the clock edge, and events are therefore now quantized to the timing edges of the clock. Second, being digital elements, the values of amplitude of their outputs are now just 0 or 1, rather than the original analog qualities. This may be contrasted to a transmission line: a delay line constructed from a transmission line can pass any signal amplitude and can make an output transition between continuous levels at any time.
A semi-analog FIR filter thus has the benefit of a digital delay line, and is thus practical to build on a silicon chip. The delay elements may, for example, be clocked D-flip-flops (DFFs) where the delay time is defined by a common clock, or simply logic gates in which the delay time is the logic gate transition time (known as the “gate delay”).
Using such a semi-analog FIR filter allows any signal that may be conveniently represented in a digital form to be processed by the filter. For example, a square wave signal at 100 megahertz (MHz) may be fed into a delay line consisting of logic gates and the output of the gates summed with the appropriate weighting to make an analog output, and, with the appropriate weightings of Wi, may even generate an analog sine wave from the digital square wave.
One particular group of signals that are often used with a semi-analog FIR filter are those generated by a sigma-delta (ΣΔ) modulator. A ΣΔ modulator creates a sequence of digital signals that change only at specific times, i.e., on the edges of an input clock to the ΣΔ modulator. Such a sequence of digital signals may be easily applied to a semi-analog FIR filter having either a DFF or gate-delay based delay line. The use of a ΣΔ modulator is convenient since it is a device that quantizes the analog signal at its input in both amplitude (0 or 1) and time (the edges of its clock). Since the ΣΔ modulator renders the analog signal into a quantized-in-amplitude and quantized-in-time signal, it is not a trivial matter to apply the resulting signal to the semi-analog FIR filter with delay elements that are clocked at the same rate as the ΣΔ modulator clock.
Since the combination of a ΣΔ modulator and semi-analog FIR filter may accept an analog signal, generate an intermediate digital pulse stream, delay that pulse stream in a simple digital delay line, and then sum the weighted signals to create an analog output, this allows for an analog-in to analog-out filter. The commercial value of such a filter is significant, in that a band-limiting filter constructed from SAW devices may be replaced by a combined ΣΔ modulator and semi-analog FIR filter and implemented on a silicon chip. This reduces cost and increases reliability, since no interconnection from a chip to a SAW is required. Further, the insertion losses that are commonly associated with SAW filters are not present.
But ΣΔ modulators have their own issues. A ΣΔ modulator is a system that exploits “noise shaping” and works because the quantization noise present in the digital output stream is removed from the frequency band of interest. For example, a signal of 20 hertz to 20 kilohertz (1 KHz) may be encoded by a ΣΔ modulator operating with a 1.5 MHz clock. Since the clock is at a much higher frequency than the highest signal of interest, the noise may be moved (i.e., “noise shaped”) out of the audio band of 20 Hz to 20 KHz and placed in a higher frequency band near the clock frequency.
Such a ΣΔ modulator is called a “low pass” ΣΔ modulator since the noise below a small fraction of the clock is removed, and in the low frequency band of interest signals will thus be represented with insignificant noise in the output pulse stream. The ratio of the clock to the highest signal of interest (here 1.5 MHz to 20 KHz, or about 750 to 1) is referred to as the oversampling ratio (OSR). Oversampling ratios of 100 and higher are typical.
Other types of ΣΔ modulators exist as well. By carefully choosing the filter in the noise shaping loop of the ΣΔ modulator it is possible to make a “band pass” ΣΔ modulator, in which noise is moved out of a band of interest to regions both above and below the desired signal. For example, in a television application, a ΣΔ modulator clocked at 1 gigahertz (GHz) may be used to remove noise in the range of 40 MHz to 48 MHz, and move it to the lower (0 to 40 MHz) and upper (48 MHz to 500 MHz) regions. In this case the OSR is only about 20 to 1 (1 GHz to 48 MHz). This is one benefit of band-pass ΣΔ modulators: the clock is not as much higher in frequency than the signal of interest, and the clock is thus easier to construct.
Band pass ΣΔ modulators are technically viable, and such a ΣΔ modulator might be used with a semi-analog FIR filter in the TV CSF above, rather than a more costly SAW filter. A band pass ΣΔ modulator is needed because a low pass ΣΔ modulator would need to be clocked at about 5 GHz or more to oversample a 40 MHz television signal. While this is not too fast for a clock, it is too fast for the filter, which must be analog and must operate with accuracy of about one part in 1000.
However, such a band-pass ΣΔ modulator demands a precision filter in its noise shaping loop. Thus, a CSF based on a band-pass ΣΔ modulator and a semi-analog FIR filter may become just as complex and costly as a more conventional CSF built with high order analog filter components or with SAW devices, and thus may not be commercially viable.
It would thus be advantageous to be able to implement a semi-analog FIR filter, for example on a silicon chip, without the use of a complex ΣΔ modulator or a complex filter.